LAUSR

In this paper, an adaptive method for sampling and reconstructing high-dimensional shift-invariant signals is proposed. First, the integrate-and-fire sampling scheme and an approximate reconstruction algorithm for one-dimensional bandlimited signals are generalized to shift-invariant signals. Then, a high-dimensional shift-invariant signal is reduced to be a sequence of one-dimensional shift-invariant signals along the trajectories parallel to some coordinate axis, which can be approximately reconstructed by the generalized integrate-and-fire sampling scheme. Finally, an approximate reconstruction for the high-dimensional shift-invariant signal is obtained by solving a series of stable linear systems of equations. The main result shows that the final reconstructed error is completely determined by the initial threshold in integrate-and-fire sampling scheme, which is generally very small. Copyright © 2017 John Wiley & Sons, Ltd.